Convex duality and the Skorokhod problem. I
It is considered the following problem (Skorokhod problem): given a closed set \(G\subset {\mathbb{R}}^{n}\), and a set of unit vectors \(d(x)\) at each point \(x\) on the boundary of \(G\), and a path \(\psi\) taking values in \({\mathbb{R}}^{n}\), define a constrained version \(\varphi\) of \(\psi\), where the constraint mechanism acts along the direction \(d(\cdot)\) in such a way that \(\varphi\) is keeping in \(G\). The main attention is paid to the case of \(G\) being a convex polyhedron. Using convex duality the authors reformulate the geometric type solvability conditions developed earlier by one of them in order to construct Skorokhod map associated with the Skorokhod problem and to verify the Lipschitz continuity of the solution. [For part II see below].
constrained deterministic and stochastic processes
scientific article; zbMATH DE number 1398348